Question

the mean monthly rent for a one bedroom apartment without a doorman in manhattan is 2641 assume the standard deviation is 500. a real estate firm samples 100 apartment.s what is the probability that the average rent of the sample is more than 2684

Answer 1

Here, μ = 2641, σ = 50 and x = 2684. We need to compute P(X >= 2684). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (2684 - 2641)/50 = 0.86

Therefore,
P(X >= 2684) = P(z <= (2684 - 2641)/50)
= P(z >= 0.86)
= 1 - 0.8051 = 0.1949